In the arts it is often necessary to manipulate a received signal or image, for both practical and operational reasons. For instance, the signal may need to be compressed into a plurality of smaller subsets prior to some secondary operation being performed on the data such as transmission over a cable or phone wire. On the receiving end, compressed transmitted signals may eventually need to be restored or reconstructed to return the signal upon receipt to its original form. Other operations can take the form of feature detection or pattern recognition, among others. In order to manipulate the received signal or image data in these instances, mathematical operations are often performed. To achieve this, the discrete signal or image is often converted into or represented by a mathematical sequence or array of discrete values. For example, binary signals or images often take the form of discrete values of [0,1] and 8-bit gray-scale images often take the form of values in the range of [0.255]. The field of discrete signal and image processing, both theoretical and applied, is relatively dominated by mathematics in the form of specific methods and applications.
Many methods of signal or image processing use one or more applications involving filters. A filter operates by capturing a windowed observation of an image or signal. A windowed observation is a collection or vector of samples from the captured image or signal. Based on this vector, a decision, based on some formula or algorithm, is made about the image or signal at a particular position within the image or signal. In general, a filter operates on a set of signal or image samples which are mathematically written as a vector having the form of (X1, . . . , XN).
Many techniques can be found in the arts, of which the following are representative and which are hereby incorporated by reference being made thereto. For example, a filter could be employed to assign one or more specific code-words to a given sample as shown in FIG. 1, (often called vector quantization), as taught by Vector Quantization and Signal Compression, A. Gesho and R. M. Gray, 1991. A filter can also assign one or more tags to a center pixel in order to indicate that the vector represented pixels are part of a specific feature of the captured image, such as a centerline, letter, or symbol. It can also assign a new sample value to the center pixel in order to accomplish the overall goal of a restoration or enhancement of a degraded image, as taught by Enhancement and Restoration of Digital Documents, R. P. Loce and E. R. Dougherty, SPIE Press, 1997, and Enhancement of Digital Documents, R. P. Loce and E. R. Dougherty, Electronic Imaging Technology, SPIE Press 1999, and Two-Dimensional Signal and Image ProcessingJ. S. Lim, Prentice Hall, 1990. A filter can also be used to predict a sample or pixel value outside the capture window with the aim of reducing the amount of data needed to store the image. This technique is often referred to as predictive encoding as taught by Digital Image Compression Techniques, M. Rabbani and P. W. Jones, SPIE Press, 1991. A filter can be used to assign an array of fewer, more restrictive values to this observation (often referred to as either “quantization,” “thresholding,” or “dithering” as taught by Digital Halftoning for Printing and Display of Electronic Images, R. P. Loce, P. G. Roetling, and Y. W. Lin, Electronic Imaging Technology, SPIE Press, 1999. Many others are found in the known literature. Other applications of filters used in signal or image processing include, resolution conversion, object detection, speckle-removal, and edge enhancement.
Nonlinear image or signal processing is a general representation of signal or image filtering based on a logical decomposition of a filter into a set of relatively simple operators. Any windowed shift-invariant filter can be represented as a combination of simple operations called hit-or-miss transforms as taught by Nonlinear Filters for Image Processing, E. R. Dougherty and J. Astola (eds.), SPIE/IEEE Press, 1999. The term nonlinear refers to the entire class of windowed filters that includes linear filters, i.e., those filters computed by convolution.
Since filters can be highly complex and repeatedly be executed millions of times in rapid succession in order to perform a single operation on a given image or signal, what is needed in the arts are compact, efficient computing architectures directed towards this end. Efficient architectures depend on filter representations. If a filter can be broken down into its base operations, it might be possible to execute the relatively simple operations in parallel in order to achieve high-speed execution and overall efficiency.
Computational Gray-Scale Morphology on Lattices (A Comparator-Based Image Algebra) Part I: Architecture, E. R. Dougherty and D. Sinha, Real Time Imaging, Vol. 1, No. 1, 1995, teaches a computer architecture using representations that perform tests in parallel. The representational methods as taught therein express any filtering operation as a collection of logical tests or operations wherein each logical test is associated with a value. If a windowed observation satisfies a test, the filter output is then associated with that value. Although the above architecture is not practical for filters requiring many tests, it does teach general representational method.
It is the aim of the present invention to overcome the conventional prior art print limitations, as described above, by programming a computational architecture to perform logical comparisons in a more compact and efficient way.